Russian news agencies say Vladimir Putin and Barack Obama have spoken on the phone and the American president has expressed his readiness to visit.
The reports said the Russian president called Obama on Tuesday to congratulate him on his re-election.
Obama "confirmed his readiness to come to Russia at a date to be agreed upon by the two sides," the state news agency RIA Novosti quoted Putin's spokesman Dmitry Peskov as saying.
Obama visited Russia as president in 2009 and met with Dmitry Medvedev, who was then the Russian president.
U.S.-Russian relations are troubled by Russia's opposition to a U.S.-backed NATO plan to place elements of a missile-defense system in Europe.
Putin also has claimed that the protest movement that arose against him the past year gets U.S. backing.